#1
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Question about Risk of Ruin
If I calculate the Risk of Ruin (with formulas provided in the past by BruceZ) and figure that my 300BB bankroll has a .5% risk of ruin, then I can assume that there is only a .5% shot that my bankroll will go bust from normal fluctuations. However, lets say that I have a bad run only due to fluctuations not bad play and lose 150 bb. Now I figure my RoR lets say to be 15%. Assuming the game conditions have not changed and I'm still playing optimally, do I still have only a .5% shot of losing my whole roll?
Edit: I think I answered my own question with a little additional thought. Can I assume that with my winrate and SD I have only a .5% chance to lose 300bb, but a 15% chance to lose 150bb? These aren't my numbers, I was just daydreaming and was wondering how the whole RoR works. |
#2
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Re: Question about Risk of Ruin
Assuming that your risk of ruin were truly 0.5% for your
initial bankroll, once your bankroll is halved, your risk of ruin (given the same game conditions, i.e., same SD and win rate) should now be exp(ln(0.005)/2) = 0.0707 or about 7.07%. Using the formula B = -exp (-sigma**2/(2*mu)) * ln(r), in general, if the risk of ruin is initially r for the bankroll of size B and then for some reason it is reduced to aB where 0<a<1, the new risk of ruin is then exp(a ln(r)). |
#3
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Re: Question about Risk of Ruin
I think you already know the answer but think of it like this.
You have A [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/heart.gif[/img] in the BB of a NL tourney and the button goes all-in which you happily call. He shows A [img]/images/graemlins/spade.gif[/img]9 [img]/images/graemlins/diamond.gif[/img]. This is essentially where you are with a big bankroll Flop comes T [img]/images/graemlins/spade.gif[/img]8 [img]/images/graemlins/spade.gif[/img]7 [img]/images/graemlins/spade.gif[/img]. This is where you are after a bad losing streak. |
#4
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Re: Question about Risk of Ruin
By the way, that last expression is just r**a and will
apply as long as a>0 (a may also be >=1) and seems to be intuitively clear, for example, when a=2. |
#5
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Re: Question about Risk of Ruin
Consult Sklansky & Malmuths bankroll tool in Stat King.
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